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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1122g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1122.g2 | 1122g1 | \([1, 1, 1, -411787, -97932871]\) | \(7722211175253055152433/340131399900069888\) | \(340131399900069888\) | \([2]\) | \(16224\) | \(2.1271\) | \(\Gamma_0(N)\)-optimal |
1122.g1 | 1122g2 | \([1, 1, 1, -1108107, 319580601]\) | \(150476552140919246594353/42832838728685592576\) | \(42832838728685592576\) | \([2]\) | \(32448\) | \(2.4737\) |
Rank
sage: E.rank()
The elliptic curves in class 1122g have rank \(0\).
Complex multiplication
The elliptic curves in class 1122g do not have complex multiplication.Modular form 1122.2.a.g
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.